An Algorithmic Approach to Wireless Sensor Networks Localization Using Rigid Graphs

Algorithm 1

Finding the rigid quadrilateral patches.

Input: The WSN graph of the form .

Output: Rigid Quadrilateral Patches

() Build adjacency matrix adj() of the WSN graph which will possess distance of WSN nodes

    that are within . Consider cycle() and node(). Initialize , , , .

() for to no. of. nodes do

()  consider the first node

()  while adj() != 0 do

()    Add the first node to cycle()

()    make node(, cycle()) = 1

()  end while

()  Consider the 1-hop neighbor of first node.

()  while adj(cycle(), ) != 0 do

()    add this node to cycle()

()    make node(, cycle()) = 1

()  end while

()  Consider the 1-hop neighbor of the previous node.

()  while adj(cycle(), ) != 0 do

()    add the this node to cycle()

()    if cycle() == then

()      Triangle is obtained and add it to the rigid matrix

()    end if

()  end while

()  Consider the 1-hop neighbor of the previous node.

()  while adj(cycle(), ) != 0 do

()    add the this node to cycle()

()    if cycle() = then

()      Quad is obtained.

()      Check whether obtained quad satisfies Theorem 8 and Theorem 12.

(      If it satisfies, then add NODE-ID’s forming quadrilateral to the rigid matrix.

()    end if

()  end while

()  Repeat the process for all the WSN nodes.

()  Put all the quads obtained with its NODE-ID in rigid matrix.

() end for